Taylor Polynomial Exploration, Part 3
is the Taylor Polynomial of . is used to approximate . Drag the point along the -axis to change the center of expansion. Slide to change the degree. Enter a new function in the text box to change the function. Drag the point along the -axis to change the point of approximation. The error in the approximation is shown below as . Its absolute value will remain between the theoretical bounds. The value guaranteed by Taylor's Theorem is calculated in the CAS view and shown in the Graphics view on the -axis between and .
Taylor's Theorem There exists between and such that where